What is the vertex of y=-2x^2+8x-12 ?

Jan 26, 2016

${x}_{\text{vertex}} = 2$ ...I will let you find y by substitution

Explanation:

This is a real cool trick

Given: $y = - 2 {x}^{2} + 8 x - 12$

Write as $y = - 2 \left({x}^{2} - \frac{8}{2} x\right) - 12$

Consider the $- \frac{8}{2} \text{ from } - \frac{8}{2} x$

Apply this process: $\left(- \frac{1}{2}\right) \times \left(- \frac{8}{2}\right) = + \frac{8}{4} = 2$

${x}_{\text{vertex}} = 2$

You can see that this is true from the graph

Now all you have to do is substitute for x in the original equation to find y.